On the jerk in motion along a space curve

Abstract

The jerk vector of a moving particle is the third time derivative of the position vector and thus the time derivative of the acceleration vector. A useful resolution of the acceleration vector of a particle traveling along a space curve is well known in the literature due to Siacci's study in 1879. A similar resolution of the jerk vector was given as a new contribution to field by ozen and Tosun in 2019. In the present article, we take into account a particle moving on a space curve which is equipped with the Bishop frame and study the aforesaid resolution of the jerk vector for this particle. Furthermore, we have given an illustrative example to explain how the our result works.